Problem: Let $f(x) = 5x^{2}+7x+2$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $5x^{2}+7x+2 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 5, b = 7, c = 2$ $ x = \dfrac{-7 \pm \sqrt{7^{2} - 4 \cdot 5 \cdot 2}}{2 \cdot 5}$ $ x = \dfrac{-7 \pm \sqrt{9}}{10}$ $ x = \dfrac{-7 \pm 3}{10}$ $x =-\frac{2}{5},-1$